A resistive voltage divider is provided for transforming a primary voltage to a proportional secondary voltage, whereas the secondary voltage is significantly smaller than the primary voltage, for example, between 10 times and 100000 times. For practical applications, the voltage divider ratio must feature good accuracy and stability versus influences such as temperature, aging, and applied voltage. The voltage divider may consist in its simplest form of just two serial resistors, one with a high resistance value and the other with a low or lower resistance value, as compared to the high resistance value. In more advanced cases, one or both of the serial resistors can be replaced by resistive networks having respective equivalent resistance values. These resistors or corresponding resistor networks may in the following also be called high and low ohmic resistors, respectively. The suited voltage divider ratio is achieved by scaling the resistance values of the high and low ohmic resistors and in order to achieve high division ratio, the resistance value of the high ohmic resistor are significantly higher than the resistance value of the low ohmic resistor.
Resistors to be employed at elevated or high voltages feature a high resistance value in order to limit the power dissipation and large size in order to withstand high voltages. Such resistors may be manufactured using thick film technology, such as screen printing processes, which allow for economical fabrication of resistive structures with high resistivity on substrates with various dimensions ranging from small to very large. Accordingly, the length of the substrate may range from less than one millimeter up to several hundred millimeters. Thick film resistors are made of a resistive film material which is applied in form of a trace onto an insulating substrate. The ends of the trace partly overlap with electrical terminations made of a highly conductive film, which are used for the electrical connectivity of the device. The conductive and resistive material layers are sequentially deposited on an electrically insulating substrate of planar or cylindrical shape, in order to form the electrical terminations and the resistive structure respectively. Additionally, insulating layers based on materials such as glass or polymers may also be used for isolation or protection purposes. Screen printing is the method of choice for applying the various layers mainly due to low process cost, high throughput, widespread availability, and repeatable quality. The process is applied equally well with flat or cylindrical insulating substrates which may be made of ceramic material such as aluminum oxide, however glass or polymer based substrates are also used. In known techniques, only one single layer of one single material is screen printed at a time, after which time or printing process additional process steps are required such as drying and firing, before any subsequent layer can be applied. All these process steps add to the complexity and to the cost to produce a certain structure or device, and it is therefore of high interest to reduce the number of printing steps, especially as each printing step requires additional process operations and may cause errors or irregularities in the printed structures.
Various shapes of the conductive and/or resistive structures can be screen printed by preparing appropriate masks. Additionally, a trimming operation is sometimes employed to achieve the desired shape of the printed structure or to fine tune the resistance value, where material is removed or cut subsequent to the printing process. The trimming process is thus a subtractive process, in contrast to the screen printing process, which is an additive process. Trimming is performed using techniques such as laser or mechanical cutting and induces stresses in the resistive structure which impact the long term stability and causes drifts of the resistance value. After trimming, it is thus necessary to perform a high temperature stabilization operation where the resistive structures/devices are annealed over a long period of time in order to release the stresses induced by trimming. It is the case that even after several days of stabilization the stresses are not fully removed and the resistance drift is worse than of an equivalent structure which was entirely produced by direct printing without trimming. Therefore, it is desirable to avoid trimming from both cost and accuracy considerations.
Aside from low process cost and good accuracy, one further advantage of thick film technology is the widespread availability of resistive materials with a wide range of resistivity values, for example, from less than 100 mO/sq to more than 1 GO/sq. The materials with high resistivity values often have poorer performance parameters such as temperature coefficient, voltage coefficient, noise, and stability. For applications demanding good accuracy, resistors with high ohmic value are therefore manufactured by using a narrow and long trace whose aspect ratio, given by the length over the width, is as high as possible in order to allow the use of materials with lower resistivity. Moreover, the absolute voltage coefficient of resistance is inverse proportional to the length of the resistive structure, making a long trace highly suitable.
For operation at high voltage levels, the resistive structure would ensure that the intensity of the electric field is as low as possible and uniformly distributed across the full structure. High peak values of the electric field intensity shall be avoided in order to ensure low electric stress, high voltage withstand, and good accuracy/stability of the resistance value. The optimum resistive structure must therefore provide high aspect ratio and uniform distribution of the electric field intensity.
It is known to manufacture thick film resistors with very high aspect ratio by screen printing a long and narrow resistive trace with serpentine shape on flat or cylindrical substrates, as described, for example, in EP 0536895 A 1. One advantage of the serpentine pattern is that it features very low inductance which is important for fabricating structures with small resistance value and low parasitic impedances. However, when the value of the resistance needs to be large like in all high voltage applications the parasitic value of the inductance is completely negligible and the parasitic capacitance becomes more critical. The serpentine structure is well suited for applications with low voltage levels. However, they are not suitable for high voltage levels because the serpentine shape engenders very non uniform distribution of the electric field with very high maximum values.
A known serpentine resistive structure is presented in FIG. 1, where the intensity of the electric field generated in the area enclosed between alternating lines is also shown. It is easily found that the magnitude of Ez is close to zero while the magnitude of E1 reaches very high value. The alternating distribution of the electric field intensity with very low minima and very high maxima is not suitable for withstanding high voltage. That is, the serpentine structure does not distribute evenly the voltage drop and the electric field along the resistor body and only parts of the structure have to carry the full voltage stress. Moreover, a significant gap between the rounded corners of the serpentine pattern needs to be left free both for production and electrical reasons. A small gap is difficult to fabricate but will also lead to strong electric fields between the corners of the serpentine pattern and poor voltage withstand of the resistor. The serpentine structure makes therefore ineffective use of both the length and the circumference of the resistor for withstanding the applied voltage.
For operation at a certain maximum voltage, the size of the resistive structure must be sufficiently big in order to keep the high peak values of the electric field intensity under practical limits, resulting in large size and cost of the device. Additionally, the high peak values of the electric field intensity generate stresses in the resistive structure and may lead to drifts of the resistance value, and therefore poor accuracy.
A resistive structure based on a serpentine shaped trace is thus suboptimal for use at elevated voltages and the same applies to resistors or resistive voltage dividers employing such resistive structure.